Applied Statistics and Probability for Engineers

13-4 RANDOMIZED COMPLETE BLOCK DESIGN 499

13-25. In “The Effect of Nozzle Design on the Stability and

Performance of Turbulent Water Jets” (Fire Safety Journal,

Vol. 4, August 1981), C. Theobald describes an experiment in

which a shape measurement was determined for several differ-

ent nozzle types at different levels of jet efflux velocity.

Interest in this experiment focuses primarily on nozzle type,

and velocity is a nuisance factor. The data are as follows:

Nozzle Jet Efflux Velocity (m/s)

Type 11.73 14.37 16.59 20.43 23.46 28.74

1 0.78 0.80 0.81 0.75 0.77 0.78

2 0.85 0.85 0.92 0.86 0.81 0.83

3 0.93 0.92 0.95 0.89 0.89 0.83

4 1.14 0.97 0.98 0.88 0.86 0.83

5 0.97 0.86 0.78 0.76 0.76 0.75

(a) Does nozzle type affect shape measurement? Compare the

nozzles with box plots and the analysis of variance.

(b) Use Fisher’s LSD method to determine specific differ-

ences between the nozzles. Does a graph of the average

(or standard deviation) of the shape measurements versus

nozzle type assist with the conclusions?

(c) Analyze the residuals from this experiment.

13-26. In Design and Analysis of Experiments,5th edition

(John Wiley & Sons, 2001), D. C. Montgomery describes an

experiment that determined the effect of four different types

of tips in a hardness tester on the observed hardness of a

metal alloy. Four specimens of the alloy were obtained, and

each tip was tested once on each specimen, producing the

following data:

(a) Is there any difference in hardness measurements between

the tips?

• 0.50


• 1


• 0.25 0 0.25 0.50


• 2

0

1

2

Normal score

zj

Residual value

Figure 13-10 Normal probability plot of

residuals from the randomized complete

block design.

1

0.5

0

• 0.5

234

eij

Figure 13-11 Residuals by treatment.

1

0.5

0

• 0.5

234

eij

5

0.5

0

• 0.5

eij

2 4 6

yij

Figure 13-12 Residuals by block. Figure 13-13 Residuals versus .yˆij

EXERCISES FOR SECTION 13-4

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